It's really not too hard to imagine. People forget that there were some very strong right-wing currents in the US in the 20's and 30's. There were large movements that admired what the fascists and nazis were doing. The pledge of allegiance, which was originally said with a nazi-style salute to the flag, came out of this era. The Ku Klux Klan was a huge and powerful organization in the 20's(at it's peak upwards of 3% of the population were members), and some of the first eugenics movements came out of the United States. It was law in several states to sterilize mental patients. There was quite a transatlantic exchange of ideas between American and European fascists, and our treatment of the Native Americans was seen as example for how ethnic minority groups in Europe could be dealt with.
You could have a few important figures in the press and government be a little more sympathetic to the Ku Klux Klan, and prevent it from being discredited in the mid-20's. Maybe you could have a powerful, charismatic figure take control of the Klan and transform it into a NSDAP-type paramilitary group/political party and take over.
It would be hard to get rid of the official trappings of democracy and our constitutional government, but congress can easily be controlled by bribes, blackmail, threats, and propaganda as our present government proves, or it could just be eliminated as an obstacle by transferring more power to the president as has been done in OTL.